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by the family of maps ? _j,U : F(U) -> ?(U), where ? _j,U(x) is the union of all open sets V of U such that the restriction of x to V (in the sense of sheaves) is contained in j_V(G(V)).

Roughly speaking an assertion inside this topos is variably true or false, and its truth value from the viewpoint of an open subset U is the open subset of U where the assertion is true.

Presheaves

Given a small category , the category of presheaves (i.e. the functor category

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